11.- SÍSMICA Y GEOFÍSICA

Table 2 presents the number of surgery types resulting after application of our solution heuristic. As can be expected the number of resulting surgery types equals the number of different case types in the data when݇ଶ= 0 is taken. However, when ݇ଶ> 0 is taken the

number of different surgery types sharply declines. Table 3 shows the increase in the loss of information (ESS) and the volume of dummy surgeries. This data can be visualized to determine the best trade-off between ESS increase and the volume of dummy surgeries, see for an example Figure 1. It is clear that obtaining the lowest volume of dummy surgeries lead to a high increase in ESS and contrarily that the lowest increase in ESS causes a high volume of dummy surgeries.

0 0.5 1 5 10 20 T=1 General surgery 152-153 31 40 13 13 13 Gynecology 47 14 14 5 2 2 ENT 42 15 15 6 1 1 Eye surgery 22-24 10 10 10 10 10 Orthopedic surgery 86-89 17 17 5 6 6 Plastic surgery 20 16 6 6 1 1 Urology 53 22 13 13 13 5 T=2 General surgery 152-153 40 42 18 20 11 Gynecology 47 16 13 7 5 5 ENT 42 7 7 10 10 3 Eye surgery 22-24 5 5 5 5 5 Orthopedic surgery 86-89 29 19 7 7 7 Plastic surgery 20 7 7 7 2 2 Urology 53 22 23 15 15 15 k1

Table 2: Number of surgery types in the best solution found for different values of k1. Multiple solutions are denoted as a range.

6.3. Discussion

In Beatrix hospital the proposed surgery types were used as input in discussions with surgeons to determine the actual surgery types. They checked for instance whether the surgical cases that were clustered in a single surgery type could be performed by a single surgeon. This enhances easy scheduling of surgeons. Surgery types were adjusted when required, which occurs in approximately 10% of the surgery types. This was mainly because of surgeon specialization.

During discussion with surgeons and hospital administrators several other issues

0 0.5 1 5 10 20

T=1 General surgery Increase ESS 0% 1% 1% 3% 3% 3%

Volume dummy surgery 65% 13% 13% 7% 7% 7%

Gynecology Increase ESS 0% 1% 1% 8% 33% 33%

Volume dummy surgery 82% 18% 18% 6% 0% 0%

ENT Increase ESS 0% 4% 4% 19% 60% 60%

Volume dummy surgery 26% 7% 7% 4% 0% 0%

Eye surgery Increase ESS 0% 0% 0% 0% 0% 0%

Volume dummy surgery 11% 4% 4% 4% 4% 4%

Orthopedic surgery Increase ESS 0% 1% 1% 4% 7% 22%

Volume dummy surgery 37% 5% 5% 3% 3% 3%

Plastic surgery Increase ESS 0% 0% 1% 1% 11% 11%

Volume dummy surgery 75% 25% 13% 13% 0% 0%

Urology Increase ESS 0% 2% 9% 9% 9% 81%

Volume dummy surgery 79% 26% 15% 15% 15% 5%

T=2 General surgery Increase ESS 0% 0% 1% 2% 4% 5%

Volume dummy surgery 48% 11% 11% 5% 5% 5%

Gynecology Increase ESS 0% 1% 2% 11% 19% 19%

Volume dummy surgery 50% 9% 6% 3% 3% 3%

ENT Increase ESS 0% 4% 4% 6% 6% 42%

Volume dummy surgery 15% 2% 2% 2% 2% 0%

Eye surgery Increase ESS 0% 2% 2% 2% 2% 2%

Volume dummy surgery 8% 2% 2% 2% 2% 2%

Orthopedic surgery Increase ESS 0% 0% 1% 3% 3% 3%

Volume dummy surgery 21% 7% 4% 1% 1% 1%

Plastic surgery Increase ESS 0% 0% 1% 1% 5% 5%

Volume dummy surgery 38% 13% 7% 7% 0% 0%

Urology Increase ESS 0% 1% 2% 10% 10% 10%

Volume dummy surgery 68% 21% 21% 10% 10% 10%

k1

Table 3: Trade off between the increase of ESS and the volume of dummy surgeries when

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48 A method for clustering surgical cases to allow master surgical scheduling

decrease. Some surgical departments consider this as positive since the number of repetition increases accordingly. Other departments considered this as negative since surgeons would become less all-round and therefore less flexible to substitute one of their colleagues.

Another issue is whether the data of a previous year is representative for the upcoming year. We believe that in general the variability in length of stay and surgery duration in a upcoming period will be equivalent to a previous period. However, there may be trends in arrival patterns of patients. This may cause the need of adjusting frequencies of surgical cases, which in turn may cause that the solution heuristics would have produced a different set of surgery types. Beatrix hospital did expect trends in arrival patterns (for instance more hip and knee replacements). However, since such high volume surgical cases typically ended up in a surgery type without any other surgical case we have chosen to adjust frequency of surgery

types after their construction.

The frequencies of

surgery types are based on averages. Seasonal fluctuations

and other reasons cause

temporarily higher or lower demand. During such period the MSS may face over or under utilization. We study this issue in a forthcoming paper, wherein we show how to deal with this issue

by manipulating planning

horizon and assignment rules.

7. Conclusion

In this paper we suggest a method for the constructing of surgery types to allow master surgical scheduling. The method is based on Ward’s hierarchical cluster method that uses the error sum of squares as measure for the loss of information. We adjusted this model to account for the volume of dummy surgeries resulting from the clustering of surgery types, as this is important for the functioning of an MSS approach. The method was successfully applied to the case of Beatrix hospital.

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Figure 1:Visualization of the results of Orthopedic Surgery in case of an MSS cycle of one week. Volume of dummy surgeries is represented as a percentage of the total Orthopedic case volume.

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A master surgical scheduling approach for cyclic scheduling in